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This paper presents a novel and non quasi static behavioral ( black box) model of power amplifiers. It takes into account nonlinear memory effects for an accurate prediction of signal distortions and power budget in communication systems. The model topology and the model extraction procedure are described. The model proposed in this paper can be derived either from envelope simulation results of a PA circuit design or from time domain envelope measurements of a PA driven by modulated stimuli. Examples of new measurements (i.e. : dynamic AM/AM conversion characteristics) highlight nonlinear memory of SSPAs. The behavioral model proposed is very well suited for an efficient implementation in system level software packages because it consists of an extension of the complex envelope gain function. The proposed complex gain which depends on the input envelope and its first time derivatives provides a great enhancement as compared to the memoryless static complex gain derived from classical AM/AM and AM/PM conversion characteristics.